Evaluation of solving time for multivariate quadratic equation system using XL algorithm over small finite fields on GPU

Satoshi Tanaka, Chen Mou Cheng, Kouichi Sakurai

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

抄録

The security of multivariate public-key cryptography is largely determined by the complexity of solving multivariate quadratic equations over finite fields, a.k.a. the MQ problem. XL (eXtended Linearization) is an efficient algorithm for solving the MQ problem, so its running time is an important indicator for the complexity of solving the MQ problem. In this work, we implement XL on graphics processing unit (GPU) and evaluate its solving time for theMQ problem over several small finite fields, namely, GF(2), GF(3), GF(5), and GF(7). Our implementations can solve MQ instances of 74 equations in 37 unknowns over GF(2) in 36,972 s, 48 equations in 24 unknowns over GF(3) in 933 s, 42 equations in 21 unknowns over GF(5) in 347 s, as well as 42 equations in 21 unknowns over GF(7) in 387 s. Moreover, we can also solve the MQ instance of 48 equations in 24 unknowns over GF(7) in 34,882 s, whose complexity is about O(267) with exhaustive search.

本文言語英語
ホスト出版物のタイトルMathematics and Computing - ICMC 2015
編集者Debasis Giri, Ram N. Mohapatra, Dipanwita Roy Chowdhury
出版社Springer New York LLC
ページ349-361
ページ数13
ISBN(印刷版)9788132224518
DOI
出版ステータス出版済み - 1 1 2015
イベント2nd International Conference on Mathematics and Computing, ICMC 2015 - Haldia, インド
継続期間: 1 5 20151 10 2015

出版物シリーズ

名前Springer Proceedings in Mathematics and Statistics
139
ISSN(印刷版)2194-1009
ISSN(電子版)2194-1017

その他

その他2nd International Conference on Mathematics and Computing, ICMC 2015
国/地域インド
CityHaldia
Period1/5/151/10/15

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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